Have the family asked to take her home? They've been saying that their only hope is a facility in NY so it implies to me that they don't think taking her home is an option. But the hospital statement said that they would agree to anything that was legally and ethically possible. People have taken care of their brain dead at home before.
The requirement that the receiving facility communicates with the hospital doesn't sound unreasonable to me at all. It happens all the time when people are transferred from one place to another. I can't see why the receiving facility wouldn't want to talk with the hospital, to make sure they have all the information that the family might not be able to communicate and to coordinate the practicalities of the transfer.
The reasons the family or the lawyer have cited for the facilities backing out included no beds left available, fear of alienating their own doctors and Jahi not having had the surgery for a feeding tube and a trach. No doubt unwillingness to be involved with the media frenzy also figures into it.
I've not seen anything that indicates the family wishes the body be taken to their home. Only speculation I've seen that it should happen is on this forum.